%I #18 Nov 04 2020 05:55:59
%S 1,2,3,1,2,2,1,2,3,1,2,1,2,1,2,3,1,2,2,1,2,3,1,2,1,2,3,1,2,1,2,3,1,2,
%T 2,1,2,3,1,2,1,2,1,2,3,1,2,2,1,2,3,1,2,1,2,3,1,2,2,1,2,3,1,2,1,2,3,1,
%U 2,2,1,2,3,1,2,1,2,1,2,3,1,2,2,1,2,3,1,2,1,2,3,1,2,1,2,3,1,2,2,1,2,3,1,2,1,2,1,2,3,1,2,2,1,2,3,1,2
%N A ternary sequence : closed under 1 -> 123, 2 -> 12, 3 -> 2 . Start with 1 .
%H Alois P. Heinz, <a href="/A214640/b214640.txt">Table of n, a(n) for n = 1..10000</a>
%e Start: 1
%e Rules:
%e 1 --> 123
%e 2 --> 12
%e 3 --> 2
%e -------------
%e 0: (#=1)
%e 1
%e 1: (#=3)
%e 123
%e 2: (#=6)
%e 123122
%e 3: (#=13)
%e 1231221231212
%e 4: (#=29)
%e 12312212312121231221231212312
%e 5: (#=64)
%e 1231221231212123122123121231212312212312121231221231212312212312
%p S:= proc(n) option remember; `if`(n=0, [1], subs(x=[1, 2, 3][],
%p y=[1, 2][], z=2, subs(1=x, 2=y, 3=z, S(n-1))))
%p end:
%p a:= proc(n) local k;
%p for k while nops(S(k))<n do od; S(k)[n]
%p end:
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Jul 28 2012
%t SubstitutionSystem[{1 -> {1, 2, 3}, 2 -> {1, 2}, 3 -> {2}}, {1}, 6] // Last (* _Jean-François Alcover_, Nov 04 2020 *)
%Y Cf. A214260, A214641, A214642, A214644.
%K nonn,easy
%O 1,2
%A _Philippe Deléham_, Jul 23 2012